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Acquisitions - Additional Information (Details) - USD ($)
$ in Millions
12 Months Ended
Nov. 12, 2015
Jan. 31, 2017
Jan. 31, 2016
Business Acquisition [Line Items]      
Cost Method Investments   $ 117.2 $ 104.3
Goodwill   1,561.1 1,535.0
netfabb      
Business Acquisition [Line Items]      
Payments to acquire business $ 42.5    
Goodwill     36.1
Cash consideration transferred for acqusitions and business combinations     42.5
Delcam plc      
Business Acquisition [Line Items]      
Goodwill   29.8  
Series of Individually Immaterial Business Acquisitions      
Business Acquisition [Line Items]      
Payments to acquire business   87.0  
Goodwill   62.8 63.7
Cash consideration transferred for acqusitions and business combinations   $ 87.0 $ 106.8
FIT AG      
Business Acquisition [Line Items]      
Cost Method Investments $ 27.4